The bielliptic locus in genus 11

2022/09/20 by Samir Canning, Hannah Larson, Canning, Samir +1
Computer Science · Mathematics · #14C15 #14C17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2209.09715

openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Chow ring of M_g is known to be generated by tautological classes for g ≤ 9. Meanwhile, the first example of a non-tautological class on M_g is the fundamental class of the bielliptic locus in M₁₂, due to van Zelm. It remains open if the Chow rings of M₁₀ and M₁₁ are generated by tautological classes. In these cases, a natural first place to look is at the bielliptic locus. In genus 10, it is already known that classes supported on the bielliptic locus are tautological. Here, we prove that all classes supported on the bielliptic locus are tautological in genus 11. By Looijenga's vanishing theorem, this implies that they all vanish.

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